Do all Japanese women know how to arrange flowers and perform at tea ceremonies?

No. Until the end of World War II both the tea ceremony and flower arrangement were prerequisites for marriage for single woman.
At that time, getting married was virtually the only option they had.
However, as more and more women started playing an important role in the post-war society, this gradually changed, and currently both art forms are taken up only by people who are truly interested in them.
A long time ago only men were engaged in performing tea ceremonies and arranging flowers.
As an essential skill to decorate homes, flower arrangement was widely practiced among women of the warrior class in the Edo period.
The tea ceremony, which is considered to help one learn etiquette and develop mental strength, gained immense popularity in the middle of the Meiji period.